## Proceedings of the Japan Academy, Series A, Mathematical Sciences

- Proc. Japan Acad. Ser. A Math. Sci.
- Volume 93, Number 3 (2017), 13-15.

### Telescopic approach to a formula of ${_{2}}F_{1}$-series by Gosper and Ebisu

#### Abstract

By means of the telescoping method, we prove an infinite series identity with four free parameters. Its limiting case is utilized, with the help of the Pfaff transformation, not only to present a new proof for a ${_{2}}F_{1}$-series identity conjectured by Gosper (1977) and proved recently by Ebisu (2013), but also to establish an extension of the binomial series.

#### Article information

**Source**

Proc. Japan Acad. Ser. A Math. Sci. Volume 93, Number 3 (2017), 13-15.

**Dates**

First available in Project Euclid: 2 March 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.pja/1488423615

**Digital Object Identifier**

doi:10.3792/pjaa.93.13

**Subjects**

Primary: 33C20: Generalized hypergeometric series, $_pF_q$

Secondary: 05A19: Combinatorial identities, bijective combinatorics

**Keywords**

Classical hypergeometric series binomial series telescoping method Pfaff transformation

#### Citation

Chu, Wenchang. Telescopic approach to a formula of ${_{2}}F_{1}$-series by Gosper and Ebisu. Proc. Japan Acad. Ser. A Math. Sci. 93 (2017), no. 3, 13--15. doi:10.3792/pjaa.93.13. https://projecteuclid.org/euclid.pja/1488423615.